The easiest rule of thumb is to plant what your neighbors have in their yards. Since you want something to look distinctive, and not copy cat, go a block away and see if you can figure out what they have.
Then when you get home, and have all your precious cuttings in hand, make sure that they aren't invasive. I found out that some of the plants that propagate so well are deemed invasive by the different groups here in South Florida.
Won't stop me though, I have pots of the stuff in my backyard that are "shovel ready" to go in the yard.
Or you could easily take this old gentleman's idea to heart and plant a forest instead.
There was an old man who lived by a forest
As he grew older and older, he started losing his hair, until one day, on his deathbed, he was completely bald. That day, he called his children to a meeting.
He said, "Look at my hair. It used to be so magnificent, but it's completely gone now. My hair can't be saved. But look outside at the forest. It's such a lovely forest with so many trees, but sooner or later they'll all be cut down and this forest will look as bald as my hair."
"What I want you to do," the man continued, "is, every time a tree is cut down or dies, plant a new one in my memory. Tell your descendants to do the same. It shall be our family's duty to keep this forest strong."
So they did. Each time the forest lost a tree, the children replanted one, and so did their children, and their children after them. And for centuries, the forest remained as lush and pretty as it once was, all because of one man and his re-seeding heirline.